There are three companies which will take you directly from Surat Thani Airport to Koh Tao. Your other alternatives are to (1) get a taxi to one of the Donsak ferry ports to board a ferry to Koh Tao, or (2) take the Night Boat from there or (3) catch a bus from the Surat

There are two departure points in Surat Thani for direct transport connections to Koh Phi Phi: (1) Surat Thani Town. (2) Surat Thani Train Station. Koh Phi Phi does not have an airport. The closest airports are in Krabi and Phuket. If you are travelling from Surat Thani it makes little sense to travel via Phuket or Krabi